scipy.fftpack.dst¶

scipy.fftpack.
dst
(x, type=2, n=None, axis=1, norm=None, overwrite_x=False)[source]¶ Return the Discrete Sine Transform of arbitrary type sequence x.
Parameters:  x : array_like
The input array.
 type : {1, 2, 3}, optional
Type of the DST (see Notes). Default type is 2.
 n : int, optional
Length of the transform. If
n < x.shape[axis]
, x is truncated. Ifn > x.shape[axis]
, x is zeropadded. The default results inn = x.shape[axis]
. axis : int, optional
Axis along which the dst is computed; the default is over the last axis (i.e.,
axis=1
). norm : {None, ‘ortho’}, optional
Normalization mode (see Notes). Default is None.
 overwrite_x : bool, optional
If True, the contents of x can be destroyed; the default is False.
Returns:  dst : ndarray of reals
The transformed input array.
See also
idst
 Inverse DST
Notes
For a single dimension array
x
.There are theoretically 8 types of the DST for different combinations of even/odd boundary conditions and boundary off sets [1], only the first 3 types are implemented in scipy.
Type I
There are several definitions of the DSTI; we use the following for
norm=None
. DSTI assumes the input is odd around n=1 and n=N.N1 y[k] = 2 * sum x[n]*sin(pi*(k+1)*(n+1)/(N+1)) n=0
Only None is supported as normalization mode for DCTI. Note also that the DCTI is only supported for input size > 1 The (unnormalized) DCTI is its own inverse, up to a factor 2(N+1).
Type II
There are several definitions of the DSTII; we use the following for
norm=None
. DSTII assumes the input is odd around n=1/2 and n=N1/2; the output is odd around k=1 and even around k=N1N1 y[k] = 2* sum x[n]*sin(pi*(k+1)*(n+0.5)/N), 0 <= k < N. n=0
if
norm='ortho'
,y[k]
is multiplied by a scaling factor ff = sqrt(1/(4*N)) if k == 0 f = sqrt(1/(2*N)) otherwise.
Type III
There are several definitions of the DSTIII, we use the following (for
norm=None
). DSTIII assumes the input is odd around n=1 and even around n=N1N2 y[k] = x[N1]*(1)**k + 2* sum x[n]*sin(pi*(k+0.5)*(n+1)/N), 0 <= k < N. n=0
The (unnormalized) DCTIII is the inverse of the (unnormalized) DCTII, up to a factor 2N. The orthonormalized DSTIII is exactly the inverse of the orthonormalized DSTII.
New in version 0.11.0.
References
[1] (1, 2) Wikipedia, “Discrete sine transform”, http://en.wikipedia.org/wiki/Discrete_sine_transform